Did Humidifying the Baseball
Decrease the Number of Homers at Coors Field?
Howard Penn
©Craig Welling www.rockiesphotos.blogspot.com/
Figure 1
Abstract
Because Coors Field in Denver is one mile above sea level, a baseball hit there will travel
about 10% farther than one hit with the same force and angle at sea level. To partially
nullify this effect in 2002 the Colorado Rockies began humidifying the balls use there. In
this paper we show that doing so statistically reduced the number of home runs hit there.
Introduction
Coors Field, where the Colorado Rockies play, has always been regarded as a home run
friendly ballpark. It is at an altitude of approximately 5280 feet. According to the
Physics of Baseball [1], a batted ball travels approximately 10% farther at that altitude
than at sea level. Figure 2 compares the flight of two batted balls with the same initial
speed, angle of elevation, and wind speed. The lower curve represents the path if the ball
is hit at sea level and the upper curve shows the path at an altitude of 5280 feet. In the
latter case the ball clears the fence but not in the former.
[5] ©James Carr http://faculty.tcc.fl.edu/scma/carrj/Java/baseball4.html
Figure 2
The Rockies were aware of this when Coors field was built. The ballpark has among the
largest average dimensions of any major league ballpark. Figure 3 is a photo of opening
day [4]
©Ballparks of Baseball www.ballparksofbaseball.com
Figure 3
Table 1 shows a comparison of the distance and height of the fences at Coors with Safeco
Field in Seattle, AT&T Ballpark in San Francisco, and Yankee Stadium (both the old and
new Yankee Stadiums have the identical dimensions) [3]. Safeco and AT&T are
considered to be ballparks that favor pitchers.
Stadium
LF HT LC
HT CF HT RC HT RF HT
Coors Field
347 8
390
8
415
8
375 17 350 17
Safeco Field
331 8
390
8
405
8
386
8 326 8
AT&T (2004) 339 8
364
11
399
8
421
8 309 25
Yankee Stadium 318 8
399 7 408 13.83 353 14.5 314 10
Table 1
In an attempt to compensate for the extra distance that batted balls fly, in 2002 the
Rockies began humidifying the baseballs. They keep them in a room where the
temperature is 70 degrees and the humidity is 50%, conditions that are similar to those at
ballparks at sea level. The idea is that the humidity will make the baseballs slightly
larger and softer, so they would not fly as far. Figure 4 shows Jay Alves, the vice
president of marketing in the Humidor.
© AP PHOTO/ED ANDRIESKI
Figure 4
The Numbers
From 1999 to 2001, 816 home runs were hit at Coors Field (an average 272 per year).
From 2002 to 2008, 1380 home runs were hit there [6, 7] (an average 197.1 per year), a
decrease of nearly 75 home runs per year. Most papers about this [2] conclude that
humidifying decreases the number of home runs. We claim that the analysis is not
sufficient. The Rockies could have traded for better pitchers, giving up home run hitters
in the exchange. Anyone who follows baseball would consider that unlikely. Maybe
testing for performance enhancing drugs cut down the number of home runs throughout
baseball. Perhaps the balls were different in the latter years. A deeper analysis is needed
to determine whether the humidifying was the cause of the decrease in home runs.
A Useful Statistic
The possible factors can be accounted for by comparing the number of home runs hit in
Rockies home games by both teams with the number hit in away games. Teams play 81
home and 81 away games. The opponents are, more or less, the same for both. (There are
a few inter-league games where the Rockies play a team only at home or only away.)
The opponent’s pitchers and batters are the same and the Rockies have the same players
for both home and away games. Therefore, if the ballpark and baseballs are homer
neutral, then home runs should be just as likely to be hit at home or away. Hence the
proportion of homers hit in home games should have a binomial distribution with mean
p=0.5. From 1999 to 2001 the number of home runs in Rockies away games was 478.
This gives the percentage of home runs in home games as 63.06%.
We can now use the large sample test for population proportion [8]:
H 0 : p = p0
pˆ - p0
z=
p0 (1 - p0 )
n
H a : p > p0 is P ( Z � z ).
We are testing the hypothesis that p0 = 0.5 . The alternate hypothesis, H a , is that the
proportion of home runs at Coors Field is significantly more that 0.5. The computation
of z is the normal approximation to the binomial distribution, whose value indicates how
many standard deviations the data is above the assumed mean. The value of P is the
probability that a set of random data will have a z value greater than or equal to the one
computed. This represents the significance level of the hypothesis test. In statistics, the
null hypothesis is usually rejected if P is less than 0.05. The data for 1999-2001 gives z =
9.40 and P( Z � 9.40) < 10 -10 . This result is significant and we can conclude that before
2002 Coors Field was definitely a ball park that favored homers. The number of home
runs for 2002-2008 in away games is 1178. So 53.95% were hit in home games. This
data gives z = 4.00 and P (Z � 4.00) » 0.000032, which is still significant.
The data indicate that we can be virtually certain that Coors Field was a home run
friendly ballpark before the team began humidifying baseballs. Although the percentage
of home runs in home games has dropped remarkably, the ballpark remains a statistically
significant home run friendly ballpark.
Comparing the two sets of data
The computations by themselves do not tell us if the drop in percentage is statistically
significant. In order to determine that we may use the significance test for comparing
two proportions [8]:
H 0 : p1 = p2
pˆ - pˆ 2
z= 1
SEDp
where the pooled standard error is
SEDp =
æ1 1 �
pˆ (1 - pˆ ) � + ÷
� n1 n2 ø
where
X + X2
pˆ = 1
n1 + n2
H a : p1 > p2 is P( Z � z ).
With our data we get
816 1386
1294
2558 = 5.40
z=
0.0168882942
and
P( Z � 5.40) »3.43 ´10-8.
The null hypothesis is that there is no significant difference between the percentages of
home runs hit in home games. The alternate hypothesis is that the difference is
significant and unlikely to have occurred by chance. The pooled standard deviation
combines both sets of data, with p̂ as the percentage of home runs in Rockies games at
home over the entire time period. This data produces a significance level of 3.43 ´10 -8 ,
which is so low that we can conclude that humidifying the baseball has decreased the
number of home runs.
Summary of Conclusions
Before the Rockies began humidifying baseballs, Coors Field was an extraordinarily
home run friendly ballpark. Since using the humidor, the ballpark remains home run
friendly despite the drop in percentage. The drop is statistically significant.
The assumption that the away games are fair is not completely correct. The Rockies are
in the same division as the San Francisco Giants and the San Diego Padres. Both of their
home ballparks are statistically significantly difficult ballparks to hit home runs. Given
the unbalanced schedule, this affects the percentage of home runs hit in the Rockies home
games. At the same time, the fact that the other two teams play a good number of away
games at Coors Field negatively affects the percentage of the season total home runs that
are hit in their home games.
Exercises
Two teams with traditionally pitcher friendly ballparks have taken steps to increase the
number of home runs in their teams home games. In 2004, the San Francisco Giants
moved the center field fence at AT&T Park in from 404 feet to 399 feet. In 2003, the
Detroit Tigers moved the left center field fence in from 395 feet to 370 feet [3]. Did that
significantly increase the number of home runs? In 2009 the Yankees opened the new
Yankee Stadium across the street from the old one. Its dimensions are exactly the same
and the ballpark was designed to make it look like the old one. Yet the feeling among
sportscasters is the number of home runs has increased. Is the new stadium statistically
more homer friendly than the old one?
The data [9]
Team
Home
Giants 1999-2003
574
Giants 2004-2008
665
Tigers 1999-2002
388
Tigers 2003-2008
1050
Yankees 1999-2008
1898
Yankees 2009
Away
861
779
572
1166
1993
References
1. R.K. Adair, Physics of Baseball, 3rd Ed. Harper-Collins, New York, NY, 2002.
2. Associated Press, “Humidor Means Coors Field is no longer a hitter’s heaven,”
available at
http://www.bostonherald.com/sports/baseball/red_sox/view.bg?articleid=1040626
3. Ballparks by Mausey and Suppes, “Dimensions of Ballparks,” available at
www.ballparks.com
4. Ballparks of Baseball, “Photo of Coors Field,” available at
www.ballparksofbaseball.com
5. J. Carr, “Tallahassee Community College, Baseball Simulator Java Applet,” available
at http://faculty.tcc.fl.edu/scma/carrj/Java/baseball4.html
6. ESPN “Major League Baseball Statistics,” available at
www.sports.espn.com/mlb/statistics
7. MLB.com, “MLB Statistics,” available at www.mlb.com/mlb/stats/index.jsp
8. D.S. Moore and G.P. McCabe, Introduction to the Practice of Statistics,
3rd Edition, W.H. Freeman and Company, New York, NY, 2000
9. H.L. Penn, “Table of home runs, 1999-2008,” unpublished.
10. Welling, Craig, “Photo of World Series Home Run,” available at
www.rockiesphotos.blogspot.com/
Howard Penn received his B.A. in Mathematics from Indiana University in 1968 and his
Masters and PhD in Mathematics from the University of Michigan in 1969 and 1973.
Since receiving his final degree, he has taught at the United States Naval Academy where
he now holds the rank of Professor. He is one of the pioneers is the use of computer
graphics in the teaching of mathematics, having written the program, MPP, which was
widely used internationally. He is also interested in finding applications of the
mathematics to areas that many students will find interesting. Outside of mathematics,
he is well known amateur photographer with special interests in wildlife, landscapes and
abstract photography. His work may be viewed at
www.flickr.com/photos/howardpennphoto